Those skilled in the arts of processing liquids desire to know how much air and/or other gases are entrapped and dissolved therein for a variety of reasons. Entrapped air can cause undesired foaming during processing, e.g. in papermaking and in the preparation of foodstuffs, and can result in disruption of film products, e.g. from paints. Entrained gases distort such processing parameters as density, making precise control of processes impossible. U.S. Pat. No. 5,365,435 illustrates the utilization of slurry density determination in fluid processing at an oil well site.
Those skilled in the art know that, generally, the more viscous a fluid being processed, the more difficult it is for any entrained air to escape from it and consequently the greater the amount of air bubbles likely to be accumulated therein. Also, as pressure on a fluid is lowered or temperature of a fluid is raised, dissolved air or other gas therein tends to leave solution and form bubbles in the fluid.
There are a number of instruments that are currently commercially available for measuring the air or gas content in a liquid. Such instruments include Metso's COLORMAT, Mütek's GAS-60, BTG's CCA 3000, Papec's PULSE))))AIR, Capella Technology's CAPTAIR, Anton-Paar's CARBO 2100 CO2 analyzer, and CyberMetrics' AIR TESTER.
Mütek's GAS-60, for instance, is said to be useful in the context of minimizing pinholes (voids) in papermaking processes. Pinholes develop when pressure is reduced and dissolved gases—which accumulate in the papermaking process due to mechanical effects and chemical and biological reactions˜are released. The GAS 60 is installed on line and is used to determine the gas content of entrained and dissolved gases in pulp suspensions. Having determined gas content, process engineers are able to calculate how much (expensive) deaerating additive should be used, and thus to avoid unnecessarily increased manufacturing costs due to employing too much deaerating additive.
Papec's PULSE))))AIR_V3 is a sensor for the measurement of entrained air and gases in process fluids. It is said to be useful in the pulp and paper industry in connection with machine headboxes and white water systems, coatings, and brownstock washers, in the secondary fiber industry (for effluent treatment), in the paint industry, in oil bottling processes, in the processing of well drilling muds, and in general in any application needing entrained air information.
Anton-Paar's CARBO 2100 CO2 analyzer employs a patented impeller method which is said to make it significantly faster that other commercially available systems for measuring and monitoring tasks and also for regulating the CO2 content of process liquids during production runs in the beer and soft drink industry.
It is believed that all of these instruments adopt a common approach, using Boyle's Law. Boyle's law is given by the equationP1V1=P2V2  (1) where V1 and V2 are the volumes of the entrained gas in the liquid at two different pressures, P1 and P2, respectively. This common approach measures the volume difference ΔV=V1−V2 between P1 and P2, and calculates the volumes of entrained gas, V1 and V2, from Boyle's Law as                               V          1                =                                                                              P                  2                                ⁢                Δ                ⁢                                                                   ⁢                V                                                              P                  2                                -                                  P                  1                                                      ⁢                                                   ⁢            and            ⁢                                                   ⁢                          V              2                                =                                                                      P                  1                                ⁢                Δ                ⁢                                                                   ⁢                V                                                              P                  2                                -                                  P                  1                                                      .                                              (        2        )            
More general formulas, which correlate the volumes of entrained gas with the pressures being acted upon, can be derived from the Ideal Gas Law asP1V1=n1RT1  (3) and P2V2=n2RT2  (4) where R is the gas constant, and n1, T1 and n2, T2 are moles of entrained gas and temperatures at P1 and P2, respectively. In the case of n1=n2 and T1=T2, equations (3) and (4) can be simplified to the equation of Boyle's Law given in (1). Hence, Boyle's Law is, in fact, a special case of the Ideal Gas Law and is valid only if the moles of entrained gas and temperatures at P1 and P2 are kept constant.
Incidentally, ΔV—that is, change in volume—can be determined either by directly measuring volumes and/or changes in volume or indirectly by measuring changes in apparent density.
In practice, a portion of the gas in a fluid will be dissolved in that fluid. At equilibrium, the solubility of gas is, as a general rule, proportional to the gas pressure as stated in Henry's LawP=Hnd  (5) where P, H, nd are the pressure of the gas being dissolved, the constant of Henry's Law, and moles of dissolved gas, respectively. This unquestionably makes n1≠n2 between two different pressures, P1 and P2, causing a violation of Boyle's Law.
Therefore, using Boyle's Law for gas-liquid mixtures, in which the occurrence of gas dissolving/exsolving is inevitable, is only an approximation of the Ideal Gas Law. The accuracy of such an approximation is directly affected by the amount of dissolved/exsolved gas. This means that using Boyle's Law in the traditional approach, where the measurements are usually taken at two equilibrium states as commonly practiced in the prior art, would maximize the error for entrained gas calculation since the amount of dissolved/exsolved gas would be maximized between the two equilibrium measurement points.
To cure this error, there have been some attempts to use Henry's Law to compensate for the amount of the dissolved gas. This approach, however, is generally impractical, inasmuch as the constants of Henry's Law are not available for many process liquids, particularly for those containing multiple-components such as coating slurries. Using the known constant of one liquid to approximate the constant of the others may potentially introduce a considerable amount of error, because the solubility of gases such as air changes dramatically from liquid to liquid. The solubility of air in isooctane at standard temperature and pressure, for example, is more than 100 times higher than the solubility of air in water.
The present inventors had previously developed a method for the improved control of continuous processes that handle liquids, which method is disclosed in U.S. patent application Ser. No. 10/046,240 (filed Jan. 16, 2002). In that method, the amount of gas in a liquid is determined by subjecting a mixture of an incompressible liquid sample and a compressible gas to three or more different equilibrium pressure states, measuring the temperature and volume of the mixture at each of the pressure states, determining the changes in volume of the mixture between at least two different pairs of pressure states, and calculating the amount of gas in the liquid sample.